Dynamic properties and numerical simulations of a fractional phytoplankton-zooplankton ecological model

It is always a difficult and hot topic to effectively explore the dynamic behavior of phytoplankton-zooplankton models. Thus, we investigated dynamic properties and a numerical solution of a fractional-order phytoplankton-zooplankton ecological model (PZEM) that incorporates the effects of toxic substances and additional food transmission in the environment. First, stability, Turing instability, Hopf bifurcation, and weakly nonlinear analysis were analyzed for the PZEM. Second, a new high-precision numerical method was developed for the fractional PZEM without diffusion terms. We compared the method with other methods to determine the effectiveness of the present method. A discretization method was established for the PZEM with diffusion term. Finally, numerical simulation verified the feasibility of the theory. Numerical simulations showed the chaotic attractor and some novel pattern dynamical behaviors of the PZEM.